The table below gives the annual sales (in millions) of a product.



**year**

1998

1999

2000

2001

2002

2003

2004

2005

2006

**sales**

297

351

393

423

441

447

441

423

393


What was the average rate of change of annual sales

a) Between 2002 and 2003

16​    millions of dollars/year

b) Between 2002 and 2004

    millions of dollars/year

To find the average rate of change of annual sales, we use the formula for the average rate of change between two points:

\[
\text{Average rate of change} = \frac{\text{Change in sales}}{\text{Change in time}}
\]

### Part (a): Average Rate of Change Between 2002 and 2003

- **Sales in 2002**: 441 million dollars
- **Sales in 2003**: 447 million dollars

**Change in sales**:

\[
447 - 441 = 6 \text{ million dollars}
\]

**Change in time**:

\[
2003 - 2002 = 1 \text{ year}
\]

**Average rate of change**:

\[
\frac{6 \text{ million dollars}}{1 \text{ year}} = 6 \text{ million dollars/year}
\]

So, the average rate of change of annual sales between 2002 and 2003 is **6 million dollars/year**.

### Part (b): Average Rate of Change Between 2002 and 2004

- **Sales in 2002**: 441 million dollars
- **Sales in 2004**: 441 million dollars

**Change in sales**:

\[
441 - 441 = 0 \text{ million dollars}
\]

**Change in time**:

\[
2004 - 2002 = 2 \text{ years}
\]

**Average rate of change**:

\[
\frac{0 \text{ million dollars}}{2 \text{ years}} = 0 \text{ million dollars/year}
\]

So, the average rate of change of annual sales between 2002 and 2004 is **0 million dollars/year**.

Would you like any more details or have any other questions?

Here are some related questions you might find interesting:

1. What is the total change in sales from 1998 to 2006?
2. How do you interpret the negative rate of change in sales after 2003?
3. What is the overall trend in sales from 1998 to 2006?
4. How would you model this sales data with a polynomial function?
5. What is the maximum sales value, and in what year does it occur?

**Tip:** The average rate of change is a useful way to understand how a quantity is changing over time, similar to the concept of slope in algebra.

Learn how to calculate the average rate of change of annual sales between 2002 and 2004 using sales data. Understand the formula for average rate of change and its application in analyzing sales trends. Suitable for high school students and learners interested in mathematical analysis of data.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation